The characterization of small particles in terms of their properties such as size, mass, shape, as well as the associated distributions of these quantities within a sample solution, has long represented a major objective of a broad range of analytical instruments. Light scattering instrumentation plays a major role among them as the technique is absolute and does not require calibration standards. This is especially true for very small particles such as molecules, viruses, and other classes of nano-particles. A light scattering measurement of a polydisperse molecular solution will yield a weight average molar mass provided that the molecular or particle concentration is known or determined by measurement. For particles/molecules of size greater than about 20 nm, the mean square radius of the scattering particles may be derived from the measured variation of the scattered light intensity with scattering angle.
The ability to measure the distributions of mass and size present in the scattering sample has been of particular importance. In order to determine these distributions, it is necessary to separate the particles present so that the scattering properties and concentration of each separated species present may be measured separately. This separation has been achieved traditionally by processes referred to as chromatographic separation. The combination of multiangle light scattering, MALS, with chromatographic separation and concentration measurement permits the immediate determination of these distributions.
Several separation techniques have been developed for such chromatographic purposes. Foremost among them is size exclusion chromatography, SEC, which is based upon forcing the solutions through columns packed with a material causing particles/molecules of larger size to transit the column more rapidly than the smaller particles. The latter are able to penetrate deeper into the interstices of the packing matrix and spending, therefore more time therein than their larger companions.
Other frequently used separation techniques include various forms of field flow fractionation, FFF, devices add reversed phase chromatography columns. For a large range of particle/molecular sizes, few separation techniques are as effective as those provided by centrifuges in their various implementations. With the exception of the analytical ultracentrifuge, AUC, such devices cannot produce a measure of mass or size without resort to calibration standards of some type. Even the AUC, when used to deduce the mass distributions of molecular solutions, requires a considerable number of ancillary measurements as well as some assumptions concerning the particles themselves such as density and shape. Operation and interpretation of the AUC instrumentation and results requires operators with exceptional training and skills. The object of the invention described here is to establish a method and apparatus by which centrifugal devices may be used to measure, in an absolute sense, many of the properties of molecular and particle suspensions. Another objective of the invention is to simplify the subsequent analyses associated with a centrifugal separation. Still a further objective of this invention is to be able to extract more information about the separating samples achieved by the centrifugal separation processes than has heretofore been possible.
Of all the devices that may be used for measuring the sizes of particles in the nanometer range, the disk and ultra centrifuges are among those most capable of providing high-resolution separations. Despite such resolution capability, the operation of such centrifuges is generally fraught with considerable ambiguities. Most of these problems are associated with uncertainties in the derived sizes of particles since such sizes are based entirely upon the arrival times of the separated particles at a detector. By using a mixture of the unknown sample particles with particles whose sizes are precisely known, these arrival times may be calibrated to some extent. Unfortunately, despite such calibrations, small variations in temperature and rotor speed, in addition to so-called streaming phenomena, often render such calibrations questionable. Another major difficulty relates to the need to know precisely the density of the particles and that of the fluid environment in which the separation is performed. Virtually all subsequent analyses are based on the a priori assumption that the particles so-separated are homogeneous spheres. Whenever a gradient is used, its explicit density variation should be known as well. Other problems associated with determining particle size by measuring times-of-arrival at the detector include deviations of Reynolds' number in excess of 0.5%, effects of sample dispersion due to Brownian motion resulting in the spreading out of the arrival times of identical particles, band broadening dependent on the speed of separation, establishing suitable gradients to prevent streaming, overloading sample concentration, range of particle sizes in the sample, problems with deconvolution analyses, etc. Virtually all these difficulties are associated with one basic shortcoming of these devices: centrifugal separation is not an absolute measurement method for most classes of particles. In other words, with the exception of a theoretical arrival time for homogeneous spheres at the detector, once a set of particles has arrived, their size cannot be measured directly. Of course, if the particles are not homogeneous spheres, i. e. of unknown structure, even the best of prior calibration procedures can result in great uncertainties in interpretation. Centrifugal separation would appear ideally suited for the subsequent application of a multiangle light scattering, or MALS, analysis were it not for the inaccessibility of the samples. Thus, using cross flow field flow fractionation as described by Wyatt, for example, in his 1998 article “Submicrometer particle sizing by multiangle light scattering following fractionation,” that appeared in J. Colloid and Interface Science volume 197, pages 9-20, multiangle light scattering analyses of the eluant samples following separation produces detailed and accurate size and distribution information. The concept has been applied also to the analyses of samples separated by other methods including size exclusion chromatography and capillary hydrodynamic fractionation, to name a few. A centrifugal device with an accessible eluting sample following separation was developed by J. Calvin Giddings and is referred to as sedimentation field flow fractionation, or SdFFF for short. This method, described, for example by Giddings in his 1993 paper in volume 260 of Science at pages 1456 et seq., required an elaborate set of slip rings and capillaries. Other types of FFF separation techniques are also discussed in Giddings' paper. Combined with a sequential MALS measurement, the analysis of eluting samples permitted the accurate characterization of each eluting fraction of particles independent of diffusion effects. Nevertheless, the SdFFF device had neither the resolution nor dynamic range of the more conventional centrifugal separation devices and was prone to leaks within a short time of installing new seals.
Results derived from the more conventional disk centrifuge and analytical centrifuge devices are based on the optical examination of small regions within the sample volume being subjected to centrifugal forces. Remote light sources, i. e. stationary relative to the spinning samples, are synchronized to the radial motion of the sample through the incident light beam to yield some measure of particle presence in the particular region being “interrogated.” Such transmitted light beam measurements may include absorption and forward scattering measurements as well as fluorescence characteristic of some types of samples. From such measurements, further attempts are usually made to derive a size distribution of the particles present in the sample by interpreting the scattering and/or obscuration of the transmitted light beam at the detector in terms of Lorenz-Mie scattering theory, i. e. assuming the particles are homogeneous spheres. The forward-scattered light intensity is assumed to arise because such spheres of a known radius, α, have entered the incident light beam. However, such “known” size was extracted from the time of arrival of the particles based on the relation
                              D          ≈                                                    18                ⁢                η                ⁢                                                                  ⁢                                  ln                  ⁡                                      (                                          R                      /                                              R                        0                                                              )                                                                                                                        ω                  ⁡                                      (                                                                  ρ                        p                                            -                                              ρ                        f                                                              )                                                                    1                  2                                            ⁢                              t                                  1                  2                                                                    ,                            (        1        )            where D=2α is the particle diameter, ω the angular velocity of the rotor, R0 is the radius at which the sample particles were injected at time t=0, R is the radius at which they are detected, η is the fluid viscosity, and ρp and ρf are the particle and fluid specific gravities, respectively. Possible sources of error in the terms of Eq. (1) can be significant. Most importantly, Eq. (1) only applies strictly for the case of homogeneous spherical structures. In addition, the fluid density must be known at the particular temperature at which the separation is being made. For centrifugal devices operating in air, the frictional forces at such high speeds generally result in the production of an increased temperature of the sample during separation and, thereby, a decrease of the fluid density, ρf.
Perhaps the greatest source of error in deriving particle size from Eq. (1) occurs when the particle density is close to that of the medium which is the case, for example, for proteins and a variety of particles produced by emulsion polymerization. When ρp and ρf are very close, slight errors in ρp can result in significant errors in the derived particle diameter, D. In addition, of course, Eq. (1) applies only to spherical particles. For non-spherical particles, the hydrodynamic radius, rh, derived is just that of an equivalent sphere. It is another objective of this invention to provide a means by which the hydrodynamic radius of a particle passing through the detection beam may be determined far more accurately and without reference to a known particle standard, often used for centrifuge calibration. In addition to a measurement of the hydrodynamic radius, a particularly useful objective of this invention is the measurement of the so-called mean square radius. Knowledge of both of these radii often permits the derivation of the particle structure as well.
It is a further objective of this invention to provide an absolute measure of the radius of a spherical particle in the range of about 10 through 1000 nm without the use of calibration particle standards. An additional objective of this invention is to permit the accurate derivation of the particle size distributions of particles separated by centrifugal means even in the presence of significant diffusion caused by Brownian motion. Another objective of this invention is to circumvent, whenever possible, distortions in derived size distributions caused by other effects that tend to broaden the separated particle bands that appear at the detector such as systematic variations in rotor speed, changes in fluid temperature and viscosity, etc. Still another objective of this invention is the ability to measure sizes and size distributions for a broad range of inhomogeneous particles whose individual density variations may not be known a priori. Because some implementations of the disk and ultracentrifuges purport to be able to measure the concentration of very small particles directly, another objective of this invention is to be able to measure the molar mass of certain classes of molecules separated by centrifugal means. The success of the present invention to achieve these objectives depends critically upon the ability to integrate a MALS detection system into a centrifugal separation device and to use the existing features of centrifugal devices to permit more accurate analyses of the measured samples. Heretofore, such integration has neither been attempted nor considered.